To me, "disjoint union", "direct product" and "set of maps" (as a special case of "internal hom") are the central keywords in what I wrote: Concepts from category theory.
Those keywords all appeared in the context of set theory long before category theory was thought of.
Even ignoring that as a historical accident (we invented set theory before category theory), those ideas are all natural, meaningful and interesting to examine in the context of sets even if one has never heard of a category.
